Forecasts of power-transformed series

Consider a time series transformed by an instantaneous power function of the Box-Cox type. For a wide range of fractional powers, this paper gives the relative bias in original metric forecasts due to use of the simple inverse retransformation when minimum mean squared error (conditional mean) forecasts are optimal. This bias varies widely according to the characteristics of the data. A fast algorithm is given to find this bias, or to find minimum mean squared error forecasts in the original metric. The results depend on the assumption that the forecast errors in the transformed metric are Gaussian. An example using real data is given.     

Automatic monitoring of forecast errors

This paper evaluates a variety of automatic monitoring schemes to detect biased forecast errors. Backward cumulative sum (cusum) tracking signals have been recommended in previous research to monitor exponential smoothing models. This research shows that identical performance can be had with much simpler tracking signals. The smoothed-error signal is recommended for α = 0.1, although its performance deteriorates badly as α is increased. For higher α values, the simple cusum signal is recommended. A tracking signal based on the autocorrelation in errors is recommended for forecasting models other than exponential smoothing, with one exception. If the time series has a constant variance, the backward cusum should give better results.     

The approximation of long‐memory processes by an ARMA model

A mean square error criterion is proposed in this paper to provide a systematic approach to approximate a long‐memory time series by a short‐memory ARMA(1, 1) process. Analytic expressions are derived to assess the effect of such an approximation. These results are established not only for the pure fractional noise case, but also for a general autoregressive fractional moving average long‐memory time series. Performances of the ARMA(1,1) approximation as compared to using an ARFIMA model are illustrated by both computations and an application to the Nile river series. Results derived in this paper shed light on the forecasting issue of a long‐memory process. Copyright © 2001 John Wiley & Sons, Ltd.     

Level shifts,temporary changes and forecasting

The purpose of this paper is to analyze the effect of not treating Level Shift and Temporary Change outliers on the point forecasts and prediction intervals from ARIMA models. One of the principal conclusions is that the outliers of the type discussed here considerably increase the inaccuracy of point forecasts, although the latter depends not only on the time of occurrence of the outliers from the forecast origin but also on the type of ARIMA processes under consideration. However, regardless of the time of occurrence and of the type of ARIMA processes considered, Level Shifts and Temporary Changes significantly affect the width of the prediction intervals.     

Combination of forecasts in electricity demand prediction

Accurate demand prediction is of great importance in the electricity supply industry. Electricity cannot be stored, and generating plant must be scheduled well in advance to meet future demand. Up to now, where online information about external conditions is unavailable, time series methods on the historical demand series have been used for short-term demand prediction. These have drawbacks, both in their sensitivity to changing weather conditions and in their poor modelling of the daily/weekly business cycles. To overcome these problems a framework has been constructed whereby forecasts from different prediction methods and different forecasting origins can be selected and combined, solely on the basis of recent forecasting performance, with no a priori assumptions of demand behaviour. This added flexibility in univariate forecasting provides a significant improvement in prediction accuracy.     

Adaptive prediction for stochastic processes with markov jump parameters

This paper is concerned with the adaptive prediction for stochastic processes with abruptly changing parameters modelled as a finite-state Markov chain. The Markov transition matrix is assumed to be known. For the coloured noise disturbance case, it is shown that the optimal prediction algorithm requires a bank of elemental predictors running in parallel with its number growing exponentially with time. If the noise disturbance is white, it is found that the number of the elemental predictors required increases exponentially with the prediction ahead step instead of time. A suboptimal predictor is proposed with substantial reduced storage and computational requirements. Simulation examples show the good performance of the proposed algorithms.     

Small sample properties of quarterly forecast errors

There are two basic approaches used in the comparative evaluation of forecasters: (1) Statistical tests of significance of differences in error measures, (2) Ordinal rankings of forecasters. To use the first approach of statistical tests, the forecast error data must satisfy the assumptions underlying those tests. This paper examines the validity of those assumptions by enquiring into the small sample properties of the forecast error data of quarterly forecasts of the U.S. economy.     

Theory and practice of multivariate arma forecasting

We compare univariate and multivariate forecasts based on ARMA models. In theory we cannot do worse by using a multivariate model instead of a univariate one, but we can risk getting no improvement. Conditions for no improvements are discussed as well as cases where large improvements occur. The effect of estimated parameters is examined and found to be small granted that a good method of estimation is used. However, multivariate models could be very sensitive to structural changes. This is illustrated via an example involving monetary data, where the multivariate forecasts perform considerably worse than the univariate ones. This seems to put a limitation on the use of multivariate ARMA forecasting models.     

Disaggregation methods to expedite product line forecasting

This paper addresses the issue of forecasting individual items within a product line; where each line includes several independent but closely related products. The purpose of the research was to reduce the overall forecasting burden by developing and assessing schemes of disaggregating forecasts of a total product line to the related individual items. Measures were developed to determine appropriate disaggregated methodologies and to compare the forecast accuracy of individual product forecasts versus disaggregated totals. Several of the procedures used were based upon extensions of the combination of forecast research and applied to disaggregations of total forecasts of product lines. The objective was to identify situations when it was advantageous to produce disaggregated forecasts, and if advantageous, which method of disaggregation to utilize. This involved identification of the general conceptual characteristics within a set of product line data that might cause a disaggregation method to produce relatively accurate forecasts. These conceptual characteristics provided guidelines for forecasters on how to select a disaggregation method and under what conditions a particular method is applicable.     

Analysis and prediction of the population in Spain: 1910-2000

"The starting hypothesis of this paper was the actual occurrence of important interactions between demographic and socio-economic factors when trying to reach population forecasts that may be more efficient than those obtained by mere extrapolative methods. In order to be able to implement this approach to the Spanish case it has been necessary to reconstruct first the Spanish population series by age and sex groups from 1910 to 1980. Later, we proceed to obtain population forecasts using alternative modeling strategies and comment on the potential problems that the new demographic situation may have for future public policy."     

The uses and abuses of ‘consensus’ forecasts

Clemen's (1989) review of the forecast-combining literature amply illustrates both the interest in and the importance of this subject. This article stresses the tautological properties of various consensus measures that assure their success relative to most individual forecasts. It confirms the finding of earlier studies that for each specific macroeconomic variable roughly one-third of individual forecasters are more accurate than a consensus. However, each individual does relatively poorly for some variable while the consensus, in contrast, necessarily never fails relative to most individuals. These results, like most previous studies, describe consensus measures that are synthetic constructs derived from a pre-existing set of individual forecasts. Strictly speaking, this contemporaneous consensus is not available to individual forecasters when their forecasts are made. A prior consensus measure, which is in their information sets, was relatively much less accurate than the contemporaneous measure. Nevertheless, a small subset of individual forecasters were generally inferior to the known, prior consensus forecast.     

The combining of forecasts using recursive techniques with non-stationary weights

This paper evaluates six optimal and four ad hoc recursive combination methods on five actual data sets. The performance of all methods is compared to the mean and recursive least squares. A modification to one method is proposed and evaluated. The recursive methods were found to be very effective from start-up on two of the data sets. Where the optimal methods worked well so did the ad hoc ones, suggesting that often combination methods allowing ‘local bias’ adjustment may be preferable to the mean forecast and comparable to the optimal methods.     

The importance of the forecast

Careful forecasts, as accurate as possible, are central to the successful implementation of policy. There are fundamental reasons why policy makers cannot ‘play by ear’, adjusting policy quickly to each unexpected deviation in economic outcomes. Specific incidents are described where economic policy went awry because of faulty forecasts. The policy process is described in detail to show precisely where the forecast enters. Forecasting as a validation tool for establishing credibility in policy formation is analysed and discussed. Some estimated measure of forecast accuracy is presented, together with commentary on the necessary degrees of precision for successful implementation of policy.